User blog:Second soup/Cosmological polarity
(epistemic status: exploratory, not explanatory. (read: metaphorically spewing garbage onto my screen here, bear with me.)) Introduction Many cosmologies consist of things that can be ordered in at least one way. [citation needed] Often, some thing or concept sits at one end of an order and marks a point past which no position on the order exists. Such a concept is commonly called an ultimatum. Some cosmologies don't have ultimata, others have exactly one, and others have more than one, whether they are opposite ends of an order or independent ends to multiple different orders. Orders can be finitely or infinitely long, and ultimata can exist at defined points, at mathematical limits, or indeed at something else entirely. I think I've seen at least one attempt to categorize cosmologies based on their "shape", using terms like line and ray to describe how cosmologies extend through, or stop at, certain points. This sounds pretty useful, but I think a better analogy, one that allows multiple paths to coexist effectively, is to think about cosmologies like vector fields, which have singularities, or, because "singularity" is already taken as a couple of different science and speculative fiction terms, like magnetic fields, which have poles. Inspired by a very short and probably misread Discord conversation, I'm going to attempt to think about what cosmologies with different numbers of poles look like, and what this means going forward. I'll use "containment" as a default ordering for now, since it's one that a lot of people in V&D, including myself, care about at least somewhat. I swear I took vector calc at some point, honest. Apolar cosmologies The degenerate case is that a cosmology has no ultimata that end orderings, and that following any path from one object to another in an order will bring one no closer to or farther from an end. This construction seems reasonably popular in V&D among those who believe that their cosmology should not be "limited", and who see no reason to stop introducing new concepts beyond the bounds of what has already been described. In an apolar cosmology, a concept of "larger" or "smaller" can exist and can be used to compare two concepts sitting at points in our cosmological vector field; for example, you could consider vectors to point in the direction of larger and more containing structures, so passing from one structure to the structure containing it would involve drawing a field line with a positive curve integral. However, importantly, there is no single pole to which all field lines eventually converge, and since we're ignoring more complex zeroes for now, this means that you can continue ascending or descending indefinitely. Such a cosmology is, in a sense, the ultimate sandbox; no conceptual limitation arrives to mark a no-go zone of any sort. Monopolar cosmologies A monopolar cosmology has one ultimatum of note; every field line following some hierarchy within such a cosmology has at least one end at that concept. My own interpretation of V&D canon, filtered into my entry on the Cosmology Tier page, looks pretty monopolar, for example. I should explain this in a bit more detail. When you are in a monopolar cosmology, starting from any point (structure or concept), following the field line in the direction of increasing order - containment - will eventually move you either towards or away from the pole. For example, if some maximal concept like the Box is your cosmology's pole, following a path of increasing containment from any particular -verse will let you conceptually approach the Box, even if you never technically reach it; if some minimal concept like a nullverse, an antibox, or a sergepoint is your pole, doing this will always move you away, conceptually, from this point. However, only one of these things can be true in a monopolar cosmology. If the Box is defined as the largest object within a cosmology, no cosmology-wide "smallest object" exists, since following two different field lines backwards will not guarantee that they return to the same point. In other words, while a sergepoint might be the smallest object in some regions of such a cosmology, it might not be in others. In the reverse case, a cosmology where all concepts are fundamentally composed of a single concept but that does not have a maximal Box-like ultimatum is also monopolar. A mildly popular approach is to have the maximal structure also be the minimal structure in some cyclical fashion. The vector field analogy might fail a little here, but you could probably jury-rig something creative with saddle points or the circulation of a curve if you wanted to draw a cute diagram or something. Dipolar cosmologies A dipolar cosmology has two notable ultimata, which are usually on opposite ends of its cosmological field lines. Typically, I'd expect these to combine the two fundamental monopolar cosmologies mentioned above; ascending in containment will reveal a single concept containing everything, while descending in containment will reveal a single concept contained within everything. I like the dipole analogy more than a simple line segment (or however such an analogy was originally drawn) because you can have multiple field lines passing from one pole to the other; many different hierarchies can exist and even interact locally, but all of them terminate at exactly two locations. Dualism is pretty neat, I guess, though I'm not a huge fan of it. To spice things up, consider: *Both poles are "positive" or "negative"; a cosmology has two largest concepts or two smallest concepts, and none of the other. What determines which hierarchies end at each pole? *A certain dipolar cosmology is actually just two overlapping monopolar cosmologies. You could have, for example, one maximally-containing structure and one minimally-else structure. How would their hierarchies intersect? (Is this even important? Probably not for this discussion. Ah well.) Tripolar and higher-order cosmologies Obviously, if you're okay with two poles, three should seem pretty reasonable. Most ordering schemes can't nicely be divided into three extremes - two makes more sense to most humans, since it's the number of endpoints that a list has - but you could probably give this a shot. More bullet points, because it's getting late and I'm running out of energy: *A tripolar cosmology has a minimal structure, a maximal structure, and an intermediate structure that every hierarchical field line passes through. For example, everything is made of sergepoints, everything fits into the Box, and every hierarchy from one to the other includes, at some point, the concept of a universe. I wouldn't exactly expect this to happen given how most maximal ultimata work, but it could be fun for a short while. It brings to mind one of Serge's old tiers (before he tossed them), which essentially said "at this scale, everything below this point is now totally up in the air and does not have to behave like that". This kind of multipolar cosmology is a firm "no" to that sentiment. *What would happen if a list really did have three or more entirely independent endpoints? Can you represent containment as a two-dimensional array rather than a one-dimensional one? I have no idea how you'd graph this out, but getting it written down would be sure to blow a couple of minds, including potentially my own. Category:Blog posts